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Theprocedureofusingacomputerformathematicalmodellingincludesfourstandardsteps:
−
adaptationofthegeneralmathematicalmodelrepresentingabroadclassofphysicalobjects(asdescribed
inthehandbooksofphysics)tothespecificityofthemodelledobject;
−
simplificationofthemodeltoaformensuringtheminimumsufficientaccuracyofmodelling;
−
discretisationofthemodelenablingitsrepresentationinacomputerbymeansofafinitenumberof
functions,variablesandparameters;
−
formaldescriptionofthemodelinalanguageunderstandableforatargetcomputer.
Animportantelementofanymethodologyforusingcomputerstosolveengineeringtasksis,therefore,the
artofreducingthosetaskstostandardnumericalproblems,suchas:
−
approximationoffunctions,
−
solvingsystemsoflinearornonlinearalgebraicequations,
−
differentiationandintegrationoffunctionsinoneormanyvariables,
−
solvingsystemsofordinarydifferentialequations.
Theproblems,presentedinthistextbook,addressallthoseissues,especiallyiftheaccuracyofcomputingis
concerned.Theycoverabroadspectrumoftopicsdifferingincomplexityanddifficulty.Someproblems
(markedwithredasterisks)gobeyondthescopeoftypicalbasiccoursesofnumericalmethods.Theyhavebeen
includedinthistextbookwithanintentiontogiveadevelopmentalopportunitytomoretalentedstudentsandto
moreadvancedstudentswhoreturntonumericalproblemsmotivatedbytheneedsrelatedtoengineering
coursesorengineeringprojects.Inmanycases,twoorthreealternativesolutionsareproposed,notonlyto
showtheequivalenceofvariouswaysofthinking,butalsotosuggestthepossibilityofincreasingthereliability
ofengineeringdesignbyitsredundantverification.Itisdemonstrated,inaconsiderablenumberofcases,that
theanalyticalsolutionsmaybeverifiedbynumericalsolutionsandviceversa.Thisisdemonstratedbymeans
ofsimpleMATLABscriptswhichquitefrequentlyrefertotheSymbolicMathToolbox™
2.
Theconsecutivechaptersofthistextbookcontainexclusivelytheformulationsoftheproblemsandtheir
solutionsofanalyticalandnumericalnature;thelatterfrequentlysupportedbysimpleMATLABscripts.
NeithertheoreticalintroductionsnorguidelinesconcerningprogramminginMATLABareprovidedthere.
Suchcontentsmaybeeasilyfoundinthenumerousbooksavailableintheacademiclibraries.Herearesome
mostrecentexamples:
W.Bober,IntroductiontoNumericalandAnalyticalMethodswithMATLAB®forEngineersandScientists,
CRCPress,BocaRaton(USA)2013.
S.C.Chapra,R.P.Canale,NumericalMethodsforEngineers,McGraw-Hill,NewYork(USA)2015(7th
edition).
S.C.D.Chapra,AppliedNumericalMethodswithMATLABforEngineersandScientists,McGraw-Hill,New
York2018(4thedition).
J.F.Epperson,AnIntroductiontoNumericalMethodsandAnalysis,Wiley&Sons,Hoboken(USA)2013
(2ndedition).
R.S.Esfandiari,NumericalMethodsforEngineersandScientistsUsingMATLAB,CRCPress,BocaRaton
(USA)2017.
A.Gupta,NumericalMethodsusingMATLAB,Apress,NewYork(USA)2014.
Huei-HuangLee,ProgrammingandEngineeringComputingwithMATLAB2019,SDCPublications,
Mission(USA)2019.
A.Kharab,R.B.Guenther,AnIntroductiontoNumericalMethods:AMATLABApproach,CRCPress,Boca
Raton(USA)2011(3rdedition).
G.Lindfield,J.Penny,NumericalMethods:UsingMATLAB,AcademicPress(@Elsevier),London&
Oxford(UK)–SanDiego&Cambridge(USA)2019(4thedition).
B.Radi,A.ElHami,AdvancedNumericalMethodswithMatlab1:FunctionApproximationandSystem
Resolution,Wiley&Sons,London(UK)–Hoboken(USA)2018.
B.Radi,A.ElHami,AdvancedNumericalMethodswithMatlab2:ResolutionofNonlinear,Differentialand
PartialDifferentialEquations,Wiley&Sons,London(UK)–Hoboken(USA)2018.
2Theymaybeeasilyrecognisedsincetheyalwayscontainthedeclarationofsymbolicvariables(syms).
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